ORIFICE PLATE

Introduction –

Orrifice Plate is a device which is used to measure the volumetric flow rate. Bernoulli’s principle is the basic principle of working. Applying Bernoulli’s principle pressure and velocities of the fluid are related.

Detailed analysis –

It’s a thin plate which has a hole in its centre. It is kept in the midway of the flowing fluid. As it is obvious when the fluid reaches the plate it will have to pass through the small hole at the centre. Now we get the maximum convergence point which occurs close to the downstream of the orifice. The point is calledvena contracta. After the vena contracta the pressure and the velocity change one another time and the fluid expands.

Using the Bernoulli’s equation we can find the mass flow rate by calculating the pressure difference between the section of the pipe and the vena contracta.

Incompressible flow through orifice-

Assuming the fluid to be incompressible say having constant density, in viscid and laminar flow in a flat pipe which has no change in elevation. Considering no friction losses also we apply Bernoulli’s theorem we get the following equations:-

Bycontinuity equation:

or V1=Q/A1andV2=Q/A2

At last the meter coefficientCwhich is given by

Now to obtain the final results we have

We multiply the density to get the mass of the flow

The various symbols used has the following meanings

Q= volumetric flow rate (at any cross-section), m³/s

= mass flow rate (at any cross-section), kg/s

Cd= coefficient of discharge, dimensionless

C= orifice flow coefficient, dimensionless

A1= cross-sectional area of the pipe, m²

A2= cross-sectional area of the orifice hole, m²

d1= diameter of the pipe, m

d2= diameter of the orifice hole, m

β= ratio of orifice hole diameter to pipe diameter, dimensionless

V1= upstream fluid velocity, m/s

V2= fluid velocity through the orifice hole, m/s

P1= fluid upstream pressure, Pa with dimensions of kg/(m·s² )

P2= fluid downstream pressure, Pa with dimensions of kg/(m·s² )

ρ= fluid density, kg/m³

Flow of gases through orifice-

For the application over gases ,factor Y is changed . Y is I.0 the incompressible fluids , for the gases it can be found by the calculations.

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